Learning Geometric Complexes for 3D Shape Classification

Prachi Kudeshia, Muhammad Altaf Agowun, Jiju Poovvancheri

Abstract:

Geometry and topology are vital elements in discerning and describing the shape of an
object. Geometric complexes constructed on the point cloud of a 3D object capture the
geometry as well as topological features of the underlying shape space. Leveraging this
aspect of geometric complexes, we present an attention-based dual stream graph neural
network (DS-GNN) for 3D shape classification. In the first stream of DS-GNN, we
introduce spiked skeleton complex (SSC) for learning the shape patterns through comprehensive
feature integration of the point cloud’s core structure. SSC is a novel and
concise geometric complex comprising principal plane-based cluster centroids complemented
with per-centroid spatial locality information. The second stream of DS-GNN
consists of alpha complex which facilitates the learning of geometric patterns embedded
in the object shapes via higher dimensional simplicial attention. To evaluate the model’s
response to different shape topologies, we perform a persistent homology-based object
segregation that groups the objects based on the underlying topological space characteristics
quantified through the second Betti number. Our experimental study on benchmark
datasets such as ModelNet40 and ScanObjectNN shows the potential of the proposed
GNN for the classification of 3D shapes with different topologies and offers an
alternative to the current evaluation practices in this domain.